Fermion Masses as Localized Energy Functionals: A Geometric Interpretation of Higgs--Lepton Couplings

Recent evidence for the Higgs boson decay into a muon pair provides a direct probe of the Higgs coupling to second--generation charged leptons. In the Standard Model, such couplings are parametrized by Yukawa constants whose origin and hierarchical structure remain unexplained. In this work, we propose an alternative but fully compatible interpretation in which fermion masses arise from localized energy functionals associated with stable fermionic configurations, and Higgs couplings are identified with scalar susceptibilities of these configurations. Within this framework, Yukawa couplings scale automatically with fermion mass, independently of microscopic details. We show that this interpretation naturally accommodates the observed Higgs--muon coupling strength, reproduces charged--lepton mass hierarchies, and yields testable constraints for future precision Higgs measurements. The construction is purely effective, introduces no new particles or interactions, and remains fully consistent with the Standard Model at presently accessible energies.